1975 AHSME Problems/Problem 14

Problem 14

If the $whatsis$ is $so$ when the $whosis$ is $is$ and the $so$ and $so$ is $is \cdot so$ , what is the $whosis \cdot whatsis$ when the $whosis$ is $so$ , the $so$ and $so$ is $so \cdot so$ and the $is$ is two ( $whatsis, whosis, is$ and $so$ are variables taking positive values)?

$\textbf{(A)}\ whosis \cdot is \cdot so \qquad \textbf{(B)}\ whosis \qquad \textbf{(C)}\ is \qquad \textbf{(D)}\ so\qquad \textbf{(E)}\ so\text{ and }so$

Solution

From the problem, we are given:

$whatsis = so$ $whosis = is$ $so + so = is \cdot so$

We want to find what $whatsis \cdot whosis$ is when $whosis = so$ , $so + so = so \cdot so$ , and $is = 2$ .

Since $is = 2$ and $so + so = is \cdot so = so \cdot so$ (from the given), that means $so = 2$ . Now we know that $whatsis = 2$ and $whosis = 2$ as well because they are equal to $so$ and $is$ , respectively.

Plugging in the values, we get $whatsis \cdot whosis = so \cdot is = 4$ . This also means that $whatsis \cdot whosis = so + so$ .

Taking a look at the answer choices, we see that our answer is $\boxed{\textbf{(E)}\ so\text{ and }so}$ . ~jiang147369

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1975 AHSME Problems/Problem 14

Problem 14

Solution